The mean of given data is 26.

C.I.	0 - 20	20 - 40	40 - 60
f	20	x	10

Statement (1): x = 26.

Statement (2): 26 = $\dfrac{10 \times 20 + 30 \times x + 50 \times 10}{30 + x}$.

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Given:

By formula; Mean = $\dfrac{∑f.x}{∑f}$

Substituting the values, we get

$\Rightarrow 26 = \dfrac{20 \times 10 + x \times 30 + 10 \times 50}{x + 30}\\[1em] \text{So, statement 2 is true.}\\[1em] \Rightarrow 26 = \dfrac{200 + 30x + 500}{30 + x}\\[1em] \Rightarrow 26(30 + x) = 200 + 30x + 500\\[1em] \Rightarrow 780 + 26x = 700 + 30x\\[1em] \Rightarrow 30x - 26x = 780 - 700\\[1em] \Rightarrow 4x = 80 \\[1em] \Rightarrow x = \dfrac{80}{4} \\[1em] \Rightarrow x = 20$

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.